REVIEW OF TWO-ELECTRON ATOMS
By Prof. L. Kaliambos (Natural Philosopher in New Energy) September 7, 2015 In 1925 the two young Dutch physicists Uhlenbeck and Goudsmit discovered the electron spin according to which the peripheral velocity of a spinning electron is greater than the speed of light. Since this discovery invalidates Einstein’s relativity (EXPERIMENTS REJECT RELATIVITY) it met much opposition by physicists including Pauli. Under the influence of Einstein’s invalid relativity physicists believed that in nature cannot exist velocities faster than the speed of light. ( See my FASTER THAN LIGHT). So great physicists like Pauli, Heisenberg, and Dirac abandoned the natural laws of electromagnetism in favor of wrong theories including qualitative approaches under an idea of symmetry properties between the two electrons of opposite spin, which lead to many complications. Thus in the “Helium atom-Wikipedia” one reads: “Unlike for hydrogen a closed form solution to the Schrodinger equation for the helium atom has not been found. However various approximations such as the Hartree-Fock method ,can be used to estimate the ground state energy and wave function of atoms”. Under the abandonment of the well-established laws in favor of various wrong theories for the explanation of two-electron atoms, now writing in Google “Review of two-electron atoms” one can see a large number of articles which provide theories and various methods of approximations. For example in the article “The theory of two-electron atoms-RevModPhys” one reads: “Since the first attempts to calculate the helium ground state in the early days of Bohr-Sommerfeld quantization, two-electron atoms have posed a series of unexpected challenges to theoretical physics. Despite the seemingly simple problem of three charged particles with known interactions, it took more than half a century after quantum mechanics was established to describe the spectra of two-electron atoms satisfactorily. The evolution of the understanding of correlated two-electron dynamics and its importance for doubly excited resonance states is presented here, with an emphasis on the concepts introduced. The authors begin by reviewing the historical development and summarizing the progress in measuring the spectra of two-electron atoms and in calculating them by solving the corresponding Schrödinger equation numerically”. Historically, Bohr in 1913 using the correct quanta of energy E = hν of the Planck discovery (1900) and applying the well-established law of the Coulomb electric force between the proton and the electron charges developed his successful model of the hydrogen atom. Then, under the discovery of the wave nature of electron Schrodinger in 1926 developed the so-called Quantum Mechanics. Despite the enormous success of the Bohr model and the quantum mechanics of Schrodinger based on the well-established laws of electromagnetism in explaining the principal features of the hydrogen spectrum and of other one-electron atomic systems, so far, under the influence of Einstein’s contradicting relativity theories which led to the abandonment of natural laws, neither was able to provide a satisfactory explanation of the two-electron atoms. In atomic physics a two-electron atom is a quantum mechanical system consisting of one nucleus with a charge Ze and just two electrons. This is the first case of many-electron systems. The first few two-electron atoms are: Z =1 : H- hydrogen anion. Z = 2 : He helium atom. Z = 3 : Li+ lithium atom anion. Z = 4 : Be2+beryllium ion. Z = 5 : B3+ boron. Prior to the development of quantum mechanics, an atom with many electrons was portrayed like the solar system, with the electrons representing the planets circulating about the nuclear “sun”. In the solar system, the gravitational interaction between planets is quite small compared with that between any planet and the very massive sun; interplanetary interactions can, therefore, be treated as small perturbations. However, In the helium atom with two electrons, the interaction energy between the two spinning electrons and between an electron and the nucleus are almost of the same magnitude, and a perturbation approach is inapplicable. It is of interest to note that in 1993 in Olympia I presented at the international conference “Frontiers of fundamental physics” my paper “Impact of Maxwell’s equation of displacement current on electromagnetic laws and comparison of the Maxwellian waves with our model of dipolic particles ". The conference was organised by the natural philosophers M. Barone and F. Selleri, who gave me an award including a disc of the atomic philosopher Democritus, because in that paper I showed that LAWS AND EXPERIMENTS INVALIDATE FIELDS AND RELATIVITY . In the same period I tried to find not only the nuclear force and structure but also the coupling of two electrons under the application of the abandoned electromagnetic laws. For example in the photoelectric effect the absorption of light contributes not only to the increase of the electron energy but also to the increase of the electron mass because the particles of light have mass m = hν/c2. (See my DISCOVERY OF PHOTON MASS ). However the electron spin which gives a peripheral velocity greater than the speed of light cannot be affected by the photon absorption. Thus after 10 years I published my paper “Nuclear structure is governed by the fundamental laws of electromagnetism" ( 2003), by showing not only my DISCOVERY OF NUCLEAR FORCE AND STRUCTURE but also that the peripheral velocity (u >> c) of two spinning electrons with opposite spin gives an attractive magnetic force Fm stronger than the electric repulsion Fe when the two electrons of mass m and charge (-e) are at a very short separation r < 578.8 /1015 m. Because of the antiparallel spin along the radial direction the interaction of the electron charges gives an electromagnetic force Fem = Fe - Fm . Therefore in my research the integration for calculating the mutual Fem led to the following relation: Fem = Fe – Fm = Ke2//r2 – (Ke2/r4)(9h2/16π2m2c2) Of course for Fe = Fm one gets the equilibrium separation ro = 3h/4πmc = 578.8/1015 m. That is, for r < 578.8/1015 m the two electrons of opposite spin exert an attractive electromagnetic force, because the attractive Fm is stronger than the repulsive Fe . Here Fm is a spin-dependent force of short range. As a consequence this situation provides the physical basis for understanding the pairing of two electrons described qualitatively by the Pauli principle, which cannot be applied in the simplest case of the deuteron of nuclear physics, because the binding energy between the two spinning nucleons occurs when the spin is not opposite (S=0) but parallel (S=1). According to the experiments in the case of two electrons with antiparallel spin the presence of a very strong external magnetic field gives parallel spin (S=1) with electric and magnetic repulsions given by Fem = Fe + Fm So according to the well-established laws of electromagnetism after a detailed analysis of paired electrons in two-electron atoms I concluded that at r < 578.8/1015 m a motional EMF produces vibrations of paired electrons. Unfortunately today physicists in the absence of a detailed knowledge believe that the two electrons of two-electron atoms under the Coulomb repulsion between the electrons move not together as one particle but as separated particles possessing the two opposite points of the diameter of the orbit around the nucleus. In fact, the two electrons of opposite spin behave like one particle circulating about the nucleus under the rules of quantum mechanics forming two-electron orbitals in helium, beryllium etc. In my paper “Spin-spin interactions of electrons and also of nucleons create atomic molecular and nuclear structures” published in Ind. J. Th. Phys. (2008) I showed that the positive vibration energy (Ev) described in eV depends on the Ze charge of nucleus as Ev = 16.95Z - 4.1 Of course in the absence of such a vibration energy Ev it is well-known that the ground state energy E described in eV for two orbiting electrons could be given by the Bohr model as E = -27.2 Z2. So the combination of the energies of the Bohr model and the vibration energies due to the opposite spin of two electrons led to my discovery of the ground state energy of two-electron atoms given by E = -27.2 Z2 +16.95 Z - 4.1 For example the laboratory measurement of the ionization energy of H- yields an energy of the ground state E = - 14.35 eV In this case since Z = 1 we get E -27.2 + 16.95 - 4.1 = -14.35 eV In the same way writing for the helium Z = 2 we get E = - 108.8 + 32.9 - 4.1 = -79.0 eV which is equal to the laboratory measurement. In the same way we can calculate the ground state energies for the Z = 3 : Li+ ion , Z = 4 : Be2+ beryllium ion, and Z = 5 : B3+ boron. The discovery of this simple formula based on the well-established laws of electromagnetism was the first fundamental equation for understanding the energies of many-electron atoms, while various theories based on qualitative symmetry properties lead to complications. Category:Fundamental physics concepts